Details

analyze310.0ms (5.6%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
50%	50%	0.1%	3
50%	50%	0.1%	4
62.4%	37.5%	0.1%	5
62.4%	37.5%	0.1%	6
68.7%	31.2%	0.1%	7
68.7%	31.2%	0.1%	8
71.8%	28.1%	0.1%	9
71.8%	28.1%	0.1%	10
73.4%	26.5%	0.1%	11
73.4%	26.5%	0.1%	12
74.1%	25.8%	0.1%	13
74.1%	25.8%	0.1%	14

Compiler

Compiled 16 to 13 computations (18.8% saved)

sample31.0ms (0.6%)

Algorithm

1×

intervals

Results

12.0ms	194×	body	128	valid
4.0ms	16×	body	4096	valid
4.0ms	17×	body	2048	valid
2.0ms	12×	body	1024	valid
1.0ms	9×	body	512	valid
1.0ms	8×	body	256	valid

Compiler

Compiled 31 to 27 computations (12.9% saved)

simplify98.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	23	23
1	23	23

prune3.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Error

36.6b

Counts

2 → 1

Compiler

Compiled 30 to 24 computations (20% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 re re) (.f64 im im))
0.2b	(sqrt.f64 (.f64 2 (+.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
0.8b	(+.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
27.2b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite34.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`add-log-exp_binary64_2504` `pow1_binary64_2526`
7×	`*-un-lft-identity_binary64_2465`
6×	`add-sqr-sqrt_binary64_2487`
5×	`add-cube-cbrt_binary64_2500`
4×	`flip3-+_binary64_2468` `sqrt-prod_binary64_2481` `flip-+_binary64_2439` `add-exp-log_binary64_2503` `add-cbrt-cube_binary64_2501` `sqrt-div_binary64_2482`
3×	`sqrt-pow1_binary64_2483`
2×	`+-commutative_binary64_2395` `sum-log_binary64_2556` `pow1/2_binary64_2545` `associate-*r/_binary64_2407`
1×	`rem-sqrt-square_binary64_2478` `pow-prod-down_binary64_2536` `distribute-lft-out_binary64_2416`

Counts

4 → 51

Calls

4 calls:

11.0ms	(sqrt.f64 (.f64 2 (+.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
8.0ms	(+.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
5.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
5.0ms	(+.f64 (.f64 re re) (.f64 im im))

series194.0ms (3.5%)

Counts

4 → 12

Calls

4 calls:

113.0ms	(sqrt.f64 (.f64 2 (+.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))) re)))
29.0ms	(+.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
29.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
22.0ms	(+.f64 (.f64 re re) (.f64 im im))

simplify79.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	4937	1040
1	4937	1040

prune81.0ms (1.5%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	57	6	63
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	58	6	64

Error

14.7b

Counts

64 → 6

Compiler

Compiled 1322 to 603 computations (54.4% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.5b	(.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (sqrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))))
7.2b	(+.f64 (.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (sqrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))))) re)
27.2b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
27.2b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite69.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

76×	`sqrt-prod_binary64_2481`
58×	`add-sqr-sqrt_binary64_2487`
34×	`sqrt-pow1_binary64_2483`
29×	`pow1_binary64_2526`
28×	`sqrt-div_binary64_2482`
18×	`*-un-lft-identity_binary64_2465` `pow1/2_binary64_2545` `add-cube-cbrt_binary64_2500`
15×	`swap-sqr_binary64_2432`
10×	`rem-sqrt-square_binary64_2478`
9×	`flip3-+_binary64_2468` `flip-+_binary64_2439` `unswap-sqr_binary64_2433` `associate-r_binary64_2405` `pow-prod-up_binary64_2535` `associate-l_binary64_2406`
6×	`add-log-exp_binary64_2504` `add-exp-log_binary64_2503` `add-cbrt-cube_binary64_2501`
5×	`pow-prod-down_binary64_2536` `pow-sqr_binary64_2438`
4×	`sqr-abs_binary64_2480` `frac-times_binary64_2475`
2×	`associate-l/_binary64_2408` `associate-r/_binary64_2407`
1×	`*-commutative_binary64_2396` `+-commutative_binary64_2395` `pow-plus_binary64_2528` `sum-log_binary64_2556` `sqrt-unprod_binary64_2485` `rem-square-sqrt_binary64_2477` `pow2_binary64_2546` `prod-exp_binary64_2514` `cbrt-unprod_binary64_2498`

Counts

4 → 128

Calls

4 calls:

24.0ms	(.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (sqrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))))
17.0ms	(+.f64 (.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (sqrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))))) re)
5.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
4.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

series103.0ms (1.9%)

Counts

4 → 12

Calls

4 calls:

31.0ms	(+.f64 (.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (sqrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im))))) re)
26.0ms	(.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (sqrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))))
23.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
22.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

simplify61.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

140 → 140

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	5171	2274

prune142.0ms (2.6%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	140	0	140
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	140	6	146

Error

14.7b

Counts

146 → 6

Compiler

Compiled 3687 to 1278 computations (65.3% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.4b	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
0.4b	(/.f64 (sqrt.f64 (.f64 (.f64 im im) 2)) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)))
27.2b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
27.6b	(sqrt.f64 (.f64 (.f64 im im) 2))

rewrite48.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

51×	`add-sqr-sqrt_binary64_2487`
50×	`sqrt-prod_binary64_2481`
38×	`*-un-lft-identity_binary64_2465`
36×	`times-frac_binary64_2471`
26×	`add-cube-cbrt_binary64_2500`
12×	`difference-of-squares_binary64_2434`
11×	`pow1_binary64_2526`
9×	`associate-/r*_binary64_2409`
6×	`add-log-exp_binary64_2504` `add-exp-log_binary64_2503` `distribute-lft-out--_binary64_2417` `add-cbrt-cube_binary64_2501`
4×	`sqrt-div_binary64_2482` `sqrt-pow1_binary64_2483` `associate-/l*_binary64_2410`
3×	`cancel-sign-sub-inv_binary64_2431` `pow-prod-down_binary64_2536`
2×	`flip--_binary64_2440` `pow1/2_binary64_2545` `associate-/r/_binary64_2411` `flip3--_binary64_2469`
1×	`flip3-+_binary64_2468` `sqrt-undiv_binary64_2486` `flip-+_binary64_2439` `clear-num_binary64_2464` `cbrt-undiv_binary64_2499` `sub-neg_binary64_2458` `div-exp_binary64_2516` `div-inv_binary64_2462` `rem-sqrt-square_binary64_2478` `diff-log_binary64_2557` `frac-2neg_binary64_2476`

Counts

4 → 108

Calls

4 calls:

17.0ms	(/.f64 (sqrt.f64 (.f64 (.f64 im im) 2)) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)))
9.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
5.0ms	(sqrt.f64 (.f64 (.f64 im im) 2))
4.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

series170.0ms (3.1%)

Counts

4 → 12

Calls

4 calls:

97.0ms	(/.f64 (sqrt.f64 (.f64 (.f64 im im) 2)) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)))
28.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))) re)
23.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
22.0ms	(sqrt.f64 (.f64 (.f64 im im) 2))

simplify73.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5054	3621

prune146.0ms (2.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	115	5	120
Fresh	1	3	4
Picked	1	0	1
Done	1	0	1
Total	118	8	126

Error

9.5b

Counts

126 → 8

Compiler

Compiled 3685 to 1338 computations (63.7% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (fabs.f64 im) (/.f64 (sqrt.f64 2) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 im im) (*.f64 re re))) re))))
0.3b	(/.f64 (sqrt.f64 2) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 im im) (.f64 re re))) re)))
0.4b	(-.f64 (sqrt.f64 (+.f64 (.f64 im im) (.f64 re re))) re)
27.2b	(sqrt.f64 (+.f64 (.f64 im im) (.f64 re re)))

rewrite89.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Rules

156×	`sqrt-prod_binary64_2481`
143×	`add-sqr-sqrt_binary64_2487`
112×	`times-frac_binary64_2471`
100×	`*-un-lft-identity_binary64_2465`
72×	`add-cube-cbrt_binary64_2500`
60×	`associate-r_binary64_2405`
28×	`difference-of-squares_binary64_2434`
14×	`distribute-lft-out--_binary64_2417`
11×	`add-exp-log_binary64_2503` `add-cbrt-cube_binary64_2501`
9×	`associate-/r*_binary64_2409`
7×	`pow1_binary64_2526`
6×	`add-log-exp_binary64_2504` `sqrt-div_binary64_2482` `associate-/l*_binary64_2410`
5×	`unswap-sqr_binary64_2433`
4×	`associate-/r/_binary64_2411`
3×	`flip--_binary64_2440` `cancel-sign-sub-inv_binary64_2431` `flip3--_binary64_2469` `associate-l_binary64_2406`
2×	`cbrt-undiv_binary64_2499` `div-exp_binary64_2516` `div-inv_binary64_2462` `prod-exp_binary64_2514` `cbrt-unprod_binary64_2498`
1×	`flip3-+_binary64_2468` `sqrt-undiv_binary64_2486` `-commutative_binary64_2396` `pow1/2_binary64_2545` `flip-+_binary64_2439` `associate-r/_binary64_2407` `clear-num_binary64_2464` `sub-neg_binary64_2458` `rem-sqrt-square_binary64_2478` `diff-log_binary64_2557` `frac-2neg_binary64_2476` `pow-prod-down_binary64_2536` `sqrt-pow1_binary64_2483`

Counts

4 → 198

Calls

4 calls:

30.0ms	(.f64 (fabs.f64 im) (/.f64 (sqrt.f64 2) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 im im) (*.f64 re re))) re))))
14.0ms	(/.f64 (sqrt.f64 2) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 im im) (.f64 re re))) re)))
9.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 im im) (.f64 re re))) re)
4.0ms	(sqrt.f64 (+.f64 (.f64 im im) (.f64 re re)))

series244.0ms (4.4%)

Counts

4 → 12

Calls

4 calls:

117.0ms	(.f64 (fabs.f64 im) (/.f64 (sqrt.f64 2) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 im im) (*.f64 re re))) re))))
76.0ms	(/.f64 (sqrt.f64 2) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 im im) (.f64 re re))) re)))
29.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 im im) (.f64 re re))) re)
22.0ms	(sqrt.f64 (+.f64 (.f64 im im) (.f64 re re)))

simplify81.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

210 → 210

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	4959	6419
1	4959	6419

prune253.0ms (4.6%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	203	7	210
Fresh	2	5	7
Picked	1	0	1
Done	0	0	0
Total	206	12	218

Error

3.0b

Counts

218 → 12

Compiler

Compiled 6488 to 2249 computations (65.3% saved)

regimes1.2s (22.1%)

Accuracy

Total 16.4b remaining (87.9%)

Threshold costs 0b (0%)

Compiler

Compiled 9395 to 6300 computations (32.9% saved)

bsearch83.0ms (1.5%)

Steps

Iters	Range	Point
9	1.7431414725320761e+62	6.669349745869486e+68	2.0982341812511796e+68
9	6.221096012041714e-309	8.608594865326139e-302	6.71142159152561e-309
8	-2.478048149990556e+141	-1.6723254658902209e+137	-2.4368798138824472e+141

Iters

Range

Point

1.7431414725320761e+62

6.669349745869486e+68

2.0982341812511796e+68

6.221096012041714e-309

8.608594865326139e-302

6.71142159152561e-309

-2.478048149990556e+141

-1.6723254658902209e+137

-2.4368798138824472e+141

Compiler

Compiled 1 to 2 computations (-100% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	61	101
1	61	101

end0.0ms (0%)

sample1.9s (33.6%)

Algorithm

1×

intervals

Results

285.0ms	6084×	body	128	valid
147.0ms	522×	body	4096	valid
140.0ms	624×	body	2048	valid
74.0ms	412×	body	1024	valid
31.0ms	223×	body	512	valid
12.0ms	135×	body	256	valid

Compiler

Compiled 1321 to 880 computations (33.4% saved)

Details

analyze310.0ms (5.6%)

sample31.0ms (0.6%)

simplify98.0ms (1.8%)

prune3.0ms (0%)

localize10.0ms (0.2%)

rewrite34.0ms (0.6%)

series194.0ms (3.5%)

simplify79.0ms (1.4%)

prune81.0ms (1.5%)

localize12.0ms (0.2%)

rewrite69.0ms (1.3%)

series103.0ms (1.9%)

simplify61.0ms (1.1%)

prune142.0ms (2.6%)

localize12.0ms (0.2%)

rewrite48.0ms (0.9%)

series170.0ms (3.1%)

simplify73.0ms (1.3%)

prune146.0ms (2.7%)

localize12.0ms (0.2%)

rewrite89.0ms (1.6%)

series244.0ms (4.4%)

simplify81.0ms (1.5%)

prune253.0ms (4.6%)

regimes1.2s (22.1%)

bsearch83.0ms (1.5%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample1.9s (33.6%)

Profiling